Finding a approximate Nash Equilibrium [1]}, [2]} is a significant solution to TEGI. The best response means the strategy \(BR(\sigma _{-i})\)  that maximizes the reward of player \(i\)  when \(\sigma _{-i}\)  is given. That is, \(v_{i}(BR(\sigma _{-i}),\sigma _{-i})=\max _{\sigma _{i}^{\prime }}v_{i}(\sigma _{i}^{\prime },\sigma _{-i})\) . A Nash Equilibrium \(\sigma ^{*}\)  is a policy where all players play a best response: \(\forall p, v_{p}\left(\sigma _{p}^{*}, \sigma _{-p}^{*}\right)=\max _{\sigma _{p}^{\prime }} v_{p}\left(\sigma _{p}^{\prime }, \sigma _{-p}^{*}\right)\) . More specifically, Nash Equilibrium has been proven to exist in TEGI. The exploitability is generally used to measure the approximation error of \(\sigma =(\sigma _{1},\sigma _{2})\) :
\(expl(\sigma _{i} \mid d^{*}) = \sum _{\sigma _{i=1,2}} \max _{\sigma ^{*}_{i}} v^{i}\left(\sigma ^{*}_{-i}, \sigma _{-i} \mid d^{*}\right)\) 
